The Park Avenue Armory must really want you to know who Benjamin Appl is.

Otherwise it wouldn’t have given such significant real estate — three concerts, three Schubert masterworks — to Mr. Appl, a 36-year-old baritone who, with these performances, is making his American recital debut.

His concerts at the Armory’s intimate Board of Officers Room, which began with Schubert’s “Die Schöne Müllerin” on Sunday and continue with the composer’s “Schwanengesang” on Tuesday and “Winterreise” on Thursday, remind me of the pianist Igor Levit’s debut there in 2014. Mr. Levit made an entrance by daring to program Beethoven’s final sonatas; Mr. Appl has chosen some of the most well known, and revealing, works in the art-song repertory.

And like Mr. Levit, who pulled off his American entree with confidence and preternatural maturity, Mr. Appl presented a masterly account of “Die Schöne Müllerin.” He had the exacting attention to text of an actor, the charisma of a seasoned storyteller and an agile voice that, while not fully formed, shows promise not only for this week’s remaining concerts, but also for what I hope to be more appearances here in the years ahead.

Mr. Appl, born in Germany and based in London, comes much-hyped from Europe, as one of the last private students of the lieder master Dietrich Fischer-Dieskau and the recipient of emerging artist awards, as well as honors for his first album with Sony Classical, “Heimat,” in 2017.

He performs with the pianist James Baillieu, who on Sunday maintained clarity and avoided the muddle that often comes with “Die Schöne Müllerin” when it is transposed lower for the baritone voice. (The piece is written for a tenor’s range.)

With text by the poet Wilhelm Müller, Schubert’s song cycle — which has the dramatic breadth of theater, and a vast melodic language — tells the story of a sensitive young miller who falls in love with the beautiful miller maid of the title, but is consumed by jealousy and, lost in his dark thoughts, drowns himself in a brook.

The youthful Mr. Appl, with wide eyes and animated dimples, looked every bit the part of Müller’s Romantic hero. Over the course of the 70-minute performance his face increasingly shined with sweat and his sculpted hair lost its shape, a serendipitous parallel with the miller’s descent into histrionics.

Yet he wasn’t overly dramatic. For the most part, Mr. Appl gave a direct reading of the piece, restrained and sublime in the final “Des Baches Wiegenlied,” and rationing theatrical moments for maximum effect: the unbridled joy of “Mein!,” the breathless rage of “Der Jäger,” the disturbing turn toward madness of “Am Feierabend.”

That song — “Am Feierabend,” in which the miller is upset that his crush said good night to everyone, not to him only — showcased Mr. Appl’s greatest talents as a performer, yet revealed where he still has room to grow. His voice’s warmth didn’t quiet carry to the top of his range, and one outburst verged on barking.

But the way he navigated the song’s transformation, from disappointment to obsession, was so gripping and troublingly real, I heard people all around me exhale afterward, as if Mr. Appl had rendered them breathless.